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Block #1,252,452

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/25/2015, 6:05:21 AM Β· Difficulty 10.7835 Β· 5,578,042 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7711ad82d3dcc45ed686dfef32bc050e81d2d1106b8a3b9b92b225e635ff43ec
View on Chainz β†—

Height

#1,252,452

Difficulty

10.783496

Transactions

1

Size

207 B

Version

2

Bits

0ac89332

Nonce

2,248,679,090

Timestamp

9/25/2015, 6:05:21 AM

Confirmations

5,578,042

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

fb5821e1b6b01f23de05ca4cd34d5b3eeb01822ba294b565dc4594495e58ef22
Transactions (1)
Coinbasefb5821e1b6b01f…4594495e58ef22
1 in β†’ 1 out8.5900 XPM116 B
AJCEY9yy…tg97E6zm
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.

9.016 Γ— 10⁹⁷(98-digit number)
90165578911511511046…83137049431120593919
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
9.016 Γ— 10⁹⁷(98-digit number)
90165578911511511046…83137049431120593919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.016 Γ— 10⁹⁷(98-digit number)
90165578911511511046…83137049431120593921
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
1.803 Γ— 10⁹⁸(99-digit number)
18033115782302302209…66274098862241187839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.803 Γ— 10⁹⁸(99-digit number)
18033115782302302209…66274098862241187841
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
3.606 Γ— 10⁹⁸(99-digit number)
36066231564604604418…32548197724482375679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.606 Γ— 10⁹⁸(99-digit number)
36066231564604604418…32548197724482375681
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
7.213 Γ— 10⁹⁸(99-digit number)
72132463129209208837…65096395448964751359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.213 Γ— 10⁹⁸(99-digit number)
72132463129209208837…65096395448964751361
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
1.442 Γ— 10⁹⁹(100-digit number)
14426492625841841767…30192790897929502719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.442 Γ— 10⁹⁹(100-digit number)
14426492625841841767…30192790897929502721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,888,202 XPMΒ·at block #6,830,493 Β· updates every 60s
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