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Block #378,409

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/27/2014, 7:32:52 PM Β· Difficulty 10.4199 Β· 6,448,702 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2cef2d662e049e417c214d01bc7aebe0c30efb97fe677d6d0e8609c7f9bb06a5
View on Chainz β†—

Height

#378,409

Difficulty

10.419913

Transactions

2

Size

381 B

Version

2

Bits

0a6b7f6e

Nonce

52,272

Timestamp

1/27/2014, 7:32:52 PM

Confirmations

6,448,702

Mined by

⛏️ aRANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

083808c563aa508b102c966e2a4099a1d1baa120a375d13895cf920c16f0daf2
Transactions (2)
Coinbase2714a49c3cce5c…ae256157a610e9
1 in β†’ 1 out9.2000 XPM97 B
ANEZwy9t…E1uf5dKY
2595a414264966…d38b43f89f0a7d
1 in β†’ 1 out2.9900 XPM193 B
ARh9YMo2…2dVKj4tb
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.

6.976 Γ— 10⁹⁢(97-digit number)
69766436647956210988…42164138986830283519
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
6.976 Γ— 10⁹⁢(97-digit number)
69766436647956210988…42164138986830283519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.976 Γ— 10⁹⁢(97-digit number)
69766436647956210988…42164138986830283521
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
1.395 Γ— 10⁹⁷(98-digit number)
13953287329591242197…84328277973660567039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.395 Γ— 10⁹⁷(98-digit number)
13953287329591242197…84328277973660567041
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
2.790 Γ— 10⁹⁷(98-digit number)
27906574659182484395…68656555947321134079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.790 Γ— 10⁹⁷(98-digit number)
27906574659182484395…68656555947321134081
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
5.581 Γ— 10⁹⁷(98-digit number)
55813149318364968790…37313111894642268159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.581 Γ— 10⁹⁷(98-digit number)
55813149318364968790…37313111894642268161
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
1.116 Γ— 10⁹⁸(99-digit number)
11162629863672993758…74626223789284536319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.116 Γ— 10⁹⁸(99-digit number)
11162629863672993758…74626223789284536321
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
Circulating Supply:57,861,067 XPMΒ·at block #6,827,110 Β· updates every 60s
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