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Block #32,315

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 2:24:43 AM Β· Difficulty 7.9902 Β· 6,784,791 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b475e67d4fb0e261ab4f4105010580f5e96ea69dd18644a0852ed963c334c40
View on Chainz β†—

Height

#32,315

Difficulty

7.990178

Transactions

1

Size

196 B

Version

2

Bits

07fd7c51

Nonce

184

Timestamp

7/14/2013, 2:24:43 AM

Confirmations

6,784,791

Mined by

⛏️ P2SHASbRxSSzrfffuPGcuJ6s3bNYQdH5rkdjdH

Merkle Root

441ab20acc796b3ffcfc6f9c98a9674315755c7a8783b60d32f584dd682f9b48
Transactions (1)
Coinbase441ab20acc796b…f584dd682f9b48
1 in β†’ 1 out15.6400 XPM108 B
ASbRxSSz…H5rkdjdH
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.

6.317 Γ— 10⁸⁹(90-digit number)
63170034630751322235…59112091082747702799
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
6.317 Γ— 10⁸⁹(90-digit number)
63170034630751322235…59112091082747702799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.317 Γ— 10⁸⁹(90-digit number)
63170034630751322235…59112091082747702801
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
1.263 Γ— 10⁹⁰(91-digit number)
12634006926150264447…18224182165495405599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.263 Γ— 10⁹⁰(91-digit number)
12634006926150264447…18224182165495405601
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
2.526 Γ— 10⁹⁰(91-digit number)
25268013852300528894…36448364330990811199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.526 Γ— 10⁹⁰(91-digit number)
25268013852300528894…36448364330990811201
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
5.053 Γ— 10⁹⁰(91-digit number)
50536027704601057788…72896728661981622399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.053 Γ— 10⁹⁰(91-digit number)
50536027704601057788…72896728661981622401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,780,887 XPMΒ·at block #6,817,105 Β· updates every 60s
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