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Block #29,475

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 3:35:59 PM Β· Difficulty 7.9847 Β· 6,797,280 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ca6d7013b7a289c12e3720cbf6a214a6bc4933b07de5560f5408098a91f1b09
View on Chainz β†—

Height

#29,475

Difficulty

7.984722

Transactions

1

Size

198 B

Version

2

Bits

07fc16c4

Nonce

80

Timestamp

7/13/2013, 3:35:59 PM

Confirmations

6,797,280

Mined by

⛏️ P2SHATdcg5aGsKSGVEp9Y9eFvZwDgeu44DE6Kp

Merkle Root

50c6ef7881f44ba889ac24f64d940b75ae186b3dd82fde303fe28c5249f9074f
Transactions (1)
Coinbase50c6ef7881f44b…e28c5249f9074f
1 in β†’ 1 out15.6600 XPM108 B
ATdcg5aG…u44DE6Kp
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.

4.198 Γ— 10⁹³(94-digit number)
41982596441848744027…44089361313613942019
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
4.198 Γ— 10⁹³(94-digit number)
41982596441848744027…44089361313613942019
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.198 Γ— 10⁹³(94-digit number)
41982596441848744027…44089361313613942021
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
8.396 Γ— 10⁹³(94-digit number)
83965192883697488054…88178722627227884039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.396 Γ— 10⁹³(94-digit number)
83965192883697488054…88178722627227884041
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
1.679 Γ— 10⁹⁴(95-digit number)
16793038576739497610…76357445254455768079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.679 Γ— 10⁹⁴(95-digit number)
16793038576739497610…76357445254455768081
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
3.358 Γ— 10⁹⁴(95-digit number)
33586077153478995221…52714890508911536159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,858,198 XPMΒ·at block #6,826,754 Β· updates every 60s
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