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Block #65,355

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2013, 11:51:46 AM Β· Difficulty 8.9839 Β· 6,733,968 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
09b8d3b138b1adcdc98a4c6d17661aff0d879cdaf98b5e98720fc4f0ce5dde90
View on Chainz β†—

Height

#65,355

Difficulty

8.983938

Transactions

1

Size

201 B

Version

2

Bits

08fbe359

Nonce

85

Timestamp

7/19/2013, 11:51:46 AM

Confirmations

6,733,968

Mined by

⛏️ P2SHAGCUbq6Mxc7yQk3kiL3txXdSCgQSxWg1oL

Merkle Root

89a547c97d506e662afd4ddaba4a94f979cc6f5440d42b91de8cb28dce251bd0
Transactions (1)
Coinbase89a547c97d506e…8cb28dce251bd0
1 in β†’ 1 out12.3700 XPM110 B
AGCUbq6M…QSxWg1oL
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.

2.289 Γ— 10⁹⁢(97-digit number)
22896441030751385475…66122571545593826009
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
2.289 Γ— 10⁹⁢(97-digit number)
22896441030751385475…66122571545593826009
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.289 Γ— 10⁹⁢(97-digit number)
22896441030751385475…66122571545593826011
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
4.579 Γ— 10⁹⁢(97-digit number)
45792882061502770951…32245143091187652019
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.579 Γ— 10⁹⁢(97-digit number)
45792882061502770951…32245143091187652021
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
9.158 Γ— 10⁹⁢(97-digit number)
91585764123005541903…64490286182375304039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.158 Γ— 10⁹⁢(97-digit number)
91585764123005541903…64490286182375304041
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
1.831 Γ— 10⁹⁷(98-digit number)
18317152824601108380…28980572364750608079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.831 Γ— 10⁹⁷(98-digit number)
18317152824601108380…28980572364750608081
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:57,638,633 XPMΒ·at block #6,799,322 Β· updates every 60s
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