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Block #901,609

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2015, 5:22:42 PM Β· Difficulty 10.9410 Β· 5,912,295 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c03eafdc5c2b5e6fa23b3884ff1f83b5b76e73eb2adddc7f35ddc8f5ef5abdf5
View on Chainz β†—

Height

#901,609

Difficulty

10.941043

Transactions

2

Size

1.29 KB

Version

2

Bits

0af0e82b

Nonce

404,258,551

Timestamp

1/19/2015, 5:22:42 PM

Confirmations

5,912,295

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

67e122e4cba674fc199fd5da9ce57d0134bf41003b5d055e29fc0bb7268c2dfa
Transactions (2)
Coinbasecb89ea1333fd18…cc9ca8fe9f3a4a
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
2008ff1d9b7586…13e199a76f5b06
7 in β†’ 2 out1925.8615 XPM1.09 KB
AVWXyPUh…WgDmQ8w3AcAFW717…V1pWEX3J
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.

1.034 Γ— 10⁹⁷(98-digit number)
10344941375272017008…19068890642614951039
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
1.034 Γ— 10⁹⁷(98-digit number)
10344941375272017008…19068890642614951039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.034 Γ— 10⁹⁷(98-digit number)
10344941375272017008…19068890642614951041
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
2.068 Γ— 10⁹⁷(98-digit number)
20689882750544034016…38137781285229902079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.068 Γ— 10⁹⁷(98-digit number)
20689882750544034016…38137781285229902081
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
4.137 Γ— 10⁹⁷(98-digit number)
41379765501088068033…76275562570459804159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.137 Γ— 10⁹⁷(98-digit number)
41379765501088068033…76275562570459804161
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
8.275 Γ— 10⁹⁷(98-digit number)
82759531002176136066…52551125140919608319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.275 Γ— 10⁹⁷(98-digit number)
82759531002176136066…52551125140919608321
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
1.655 Γ— 10⁹⁸(99-digit number)
16551906200435227213…05102250281839216639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.655 Γ— 10⁹⁸(99-digit number)
16551906200435227213…05102250281839216641
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:57,755,311 XPMΒ·at block #6,813,903 Β· updates every 60s
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