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Block #29,349

TWNLength 7β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 3:13:05 PM Β· Difficulty 7.9844 Β· 6,781,539 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b14e610de3b3eb8a288c4c15d36f0814746720a8b36d01fa64cbb5638e292f94
View on Chainz β†—

Height

#29,349

Difficulty

7.984403

Transactions

1

Size

197 B

Version

2

Bits

07fc01d9

Nonce

478

Timestamp

7/13/2013, 3:13:05 PM

Confirmations

6,781,539

Mined by

⛏️ P2SHAKsLKPc8KMAFsNueJDJSs3dfp1zkBgUqcr

Merkle Root

40790262facf1b54e180df437223ec00212f81f2ab04c2dd473886d4ab7a5df4
Transactions (1)
Coinbase40790262facf1b…3886d4ab7a5df4
1 in β†’ 1 out15.6700 XPM108 B
AKsLKPc8…zkBgUqcr
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.

2.291 Γ— 10⁹²(93-digit number)
22910034838829902666…07463882560497890099
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
2.291 Γ— 10⁹²(93-digit number)
22910034838829902666…07463882560497890099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.291 Γ— 10⁹²(93-digit number)
22910034838829902666…07463882560497890101
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
4.582 Γ— 10⁹²(93-digit number)
45820069677659805332…14927765120995780199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.582 Γ— 10⁹²(93-digit number)
45820069677659805332…14927765120995780201
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
9.164 Γ— 10⁹²(93-digit number)
91640139355319610665…29855530241991560399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.164 Γ— 10⁹²(93-digit number)
91640139355319610665…29855530241991560401
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
1.832 Γ— 10⁹³(94-digit number)
18328027871063922133…59711060483983120799
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:57,731,205 XPMΒ·at block #6,810,887 Β· updates every 60s
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