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Block #2,890,316

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/21/2018, 7:31:09 AM Β· Difficulty 11.6172 Β· 3,949,107 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7473af73f21d40e996f7336e1b0ad7bfe7f0d14cdd9a8632f74c1eeed75cd7c4
View on Chainz β†—

Height

#2,890,316

Difficulty

11.617180

Transactions

1

Size

199 B

Version

2

Bits

0b9dff85

Nonce

732,345,553

Timestamp

10/21/2018, 7:31:09 AM

Confirmations

3,949,107

Mined by

⛏️ P2SHAWmJ31e14fe7XS2pGXUe5x7TiNgLeLevmV

Merkle Root

8d93cd130ce387ee967589a9fda5f97101a99aa89bffb1d9c8b6489f88114d33
Transactions (1)
Coinbase8d93cd130ce387…b6489f88114d33
1 in β†’ 1 out7.4000 XPM110 B
AWmJ31e1…gLeLevmV
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.

7.425 Γ— 10⁹¹(92-digit number)
74254989033345220110…60193258306425514559
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
7.425 Γ— 10⁹¹(92-digit number)
74254989033345220110…60193258306425514559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.425 Γ— 10⁹¹(92-digit number)
74254989033345220110…60193258306425514561
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
1.485 Γ— 10⁹²(93-digit number)
14850997806669044022…20386516612851029119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.485 Γ— 10⁹²(93-digit number)
14850997806669044022…20386516612851029121
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
2.970 Γ— 10⁹²(93-digit number)
29701995613338088044…40773033225702058239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.970 Γ— 10⁹²(93-digit number)
29701995613338088044…40773033225702058241
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
5.940 Γ— 10⁹²(93-digit number)
59403991226676176088…81546066451404116479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.940 Γ— 10⁹²(93-digit number)
59403991226676176088…81546066451404116481
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
1.188 Γ— 10⁹³(94-digit number)
11880798245335235217…63092132902808232959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.188 Γ— 10⁹³(94-digit number)
11880798245335235217…63092132902808232961
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
2.376 Γ— 10⁹³(94-digit number)
23761596490670470435…26184265805616465919
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:57,959,672 XPMΒ·at block #6,839,422 Β· updates every 60s
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