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Block #63,753

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2013, 3:24:18 AM Β· Difficulty 8.9800 Β· 6,744,285 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d29df682139d4b18d37d18ed81a89376d9124c0e1f7c22f64303450edf106e7d
View on Chainz β†—

Height

#63,753

Difficulty

8.979988

Transactions

1

Size

201 B

Version

2

Bits

08fae078

Nonce

433

Timestamp

7/19/2013, 3:24:18 AM

Confirmations

6,744,285

Mined by

⛏️ P2SHAex6Ue2dTT3srjKf1m8Yae6im3NmvAPnKJ

Merkle Root

0fe134f035c487186fa1da62db0f94e30efbf94227797a144cd1357eb6143c50
Transactions (1)
Coinbase0fe134f035c487…d1357eb6143c50
1 in β†’ 1 out12.3800 XPM109 B
Aex6Ue2d…NmvAPnKJ
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.

8.678 Γ— 10⁹⁹(100-digit number)
86781461743251256722…52533059049456824809
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
8.678 Γ— 10⁹⁹(100-digit number)
86781461743251256722…52533059049456824809
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.678 Γ— 10⁹⁹(100-digit number)
86781461743251256722…52533059049456824811
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
1.735 Γ— 10¹⁰⁰(101-digit number)
17356292348650251344…05066118098913649619
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.735 Γ— 10¹⁰⁰(101-digit number)
17356292348650251344…05066118098913649621
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
3.471 Γ— 10¹⁰⁰(101-digit number)
34712584697300502688…10132236197827299239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.471 Γ— 10¹⁰⁰(101-digit number)
34712584697300502688…10132236197827299241
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
6.942 Γ— 10¹⁰⁰(101-digit number)
69425169394601005377…20264472395654598479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.942 Γ— 10¹⁰⁰(101-digit number)
69425169394601005377…20264472395654598481
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:57,708,349 XPMΒ·at block #6,808,037 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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