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Block #3,007,668

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2019, 9:13:58 AM Β· Difficulty 11.2069 Β· 3,834,413 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4b824e36aaa1391c02af230d34b8b2d3a5a5038ad76ef1124ac8599cbebb58e2
View on Chainz β†—

Height

#3,007,668

Difficulty

11.206943

Transactions

1

Size

202 B

Version

2

Bits

0b34fa37

Nonce

34,936,172

Timestamp

1/13/2019, 9:13:58 AM

Confirmations

3,834,413

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

75877f32847dd2f21834efb784a0190d1fb267073e598101d2229aa2189b05cb
Transactions (1)
Coinbase75877f32847dd2…229aa2189b05cb
1 in β†’ 1 out7.9500 XPM110 B
AUhjokok…k5m93PZR
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.

2.961 Γ— 10⁹⁸(99-digit number)
29614872440440820933…40803454635229183999
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
2.961 Γ— 10⁹⁸(99-digit number)
29614872440440820933…40803454635229183999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.961 Γ— 10⁹⁸(99-digit number)
29614872440440820933…40803454635229184001
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
5.922 Γ— 10⁹⁸(99-digit number)
59229744880881641867…81606909270458367999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.922 Γ— 10⁹⁸(99-digit number)
59229744880881641867…81606909270458368001
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
1.184 Γ— 10⁹⁹(100-digit number)
11845948976176328373…63213818540916735999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.184 Γ— 10⁹⁹(100-digit number)
11845948976176328373…63213818540916736001
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
2.369 Γ— 10⁹⁹(100-digit number)
23691897952352656746…26427637081833471999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.369 Γ— 10⁹⁹(100-digit number)
23691897952352656746…26427637081833472001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.738 Γ— 10⁹⁹(100-digit number)
47383795904705313493…52855274163666943999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.738 Γ— 10⁹⁹(100-digit number)
47383795904705313493…52855274163666944001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
9.476 Γ— 10⁹⁹(100-digit number)
94767591809410626987…05710548327333887999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,981,032 XPMΒ·at block #6,842,080 Β· updates every 60s
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