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Block #902,740

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 1/20/2015, 2:26:19 PM Β· Difficulty 10.9395 Β· 5,900,717 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
b5d67c92e2b24ae3b9858bf2e94258e028d72cf46819988431fdc53b44c79e9d
View on Chainz β†—

Height

#902,740

Difficulty

10.939536

Transactions

2

Size

6.92 KB

Version

2

Bits

0af0856b

Nonce

1,484,352,656

Timestamp

1/20/2015, 2:26:19 PM

Confirmations

5,900,717

Mined by

⛏️ P2SHAXkkNiXVavB6cWUT5zKwA1yTQsSPVopPGR

Merkle Root

5e5036171e9ff5e1e7bd1141fcf742b05da2759493697ed5773df4d2242cc4d5
Transactions (2)
Coinbasee6dbc7318f7a47…710f7615dffc7f
1 in β†’ 1 out8.4100 XPM109 B
AXkkNiXV…SPVopPGR
e996aa560cb377…5193ff3340e76f
46 in β†’ 2 out8789.1279 XPM6.73 KB
AR2dd5Gz…2yErWs99ALh8Jn1n…6RonKSwd
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.355 Γ— 10⁹³(94-digit number)
73550581701482530981…50063481763979313219
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
7.355 Γ— 10⁹³(94-digit number)
73550581701482530981…50063481763979313219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.355 Γ— 10⁹³(94-digit number)
73550581701482530981…50063481763979313221
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.471 Γ— 10⁹⁴(95-digit number)
14710116340296506196…00126963527958626439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.471 Γ— 10⁹⁴(95-digit number)
14710116340296506196…00126963527958626441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.942 Γ— 10⁹⁴(95-digit number)
29420232680593012392…00253927055917252879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.942 Γ— 10⁹⁴(95-digit number)
29420232680593012392…00253927055917252881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.884 Γ— 10⁹⁴(95-digit number)
58840465361186024785…00507854111834505759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.884 Γ— 10⁹⁴(95-digit number)
58840465361186024785…00507854111834505761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁡(96-digit number)
11768093072237204957…01015708223669011519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.176 Γ— 10⁹⁡(96-digit number)
11768093072237204957…01015708223669011521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.353 Γ— 10⁹⁡(96-digit number)
23536186144474409914…02031416447338023039
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.353 Γ— 10⁹⁡(96-digit number)
23536186144474409914…02031416447338023041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,671,683 XPMΒ·at block #6,803,456 Β· updates every 60s
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