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Block #2,478,097

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/18/2018, 1:58:52 AM Β· Difficulty 10.9652 Β· 4,354,763 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b5289b962f340e62c6f09ca9a5d7295bbf730f302f0d5238312bd02ec10c59e
View on Chainz β†—

Height

#2,478,097

Difficulty

10.965233

Transactions

1

Size

200 B

Version

2

Bits

0af71981

Nonce

124,107,980

Timestamp

1/18/2018, 1:58:52 AM

Confirmations

4,354,763

Mined by

⛏️ P2SHAYbUoVEUf2i4MBmUPLKe5Luf1bvJDmZGka

Merkle Root

d1b9d3a5a515d8b5b49356ddb6b0f2c72b8bf2166ec90da14c4e31550a6142fe
Transactions (1)
Coinbased1b9d3a5a515d8…4e31550a6142fe
1 in β†’ 1 out8.3000 XPM110 B
AYbUoVEU…vJDmZGka
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.

1.397 Γ— 10⁹⁴(95-digit number)
13974305038304709469…15746334000006218489
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
1.397 Γ— 10⁹⁴(95-digit number)
13974305038304709469…15746334000006218489
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.397 Γ— 10⁹⁴(95-digit number)
13974305038304709469…15746334000006218491
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
2.794 Γ— 10⁹⁴(95-digit number)
27948610076609418939…31492668000012436979
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.794 Γ— 10⁹⁴(95-digit number)
27948610076609418939…31492668000012436981
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
5.589 Γ— 10⁹⁴(95-digit number)
55897220153218837879…62985336000024873959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.589 Γ— 10⁹⁴(95-digit number)
55897220153218837879…62985336000024873961
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
1.117 Γ— 10⁹⁡(96-digit number)
11179444030643767575…25970672000049747919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.117 Γ— 10⁹⁡(96-digit number)
11179444030643767575…25970672000049747921
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
2.235 Γ— 10⁹⁡(96-digit number)
22358888061287535151…51941344000099495839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.235 Γ— 10⁹⁡(96-digit number)
22358888061287535151…51941344000099495841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
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