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Block #1,371,782

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 5:53:43 PM Β· Difficulty 10.8106 Β· 5,471,142 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5030b39a5332db8c3c855392bfc4e9018f3a40a62f55f0546d83a325b7d760cf
View on Chainz β†—

Height

#1,371,782

Difficulty

10.810616

Transactions

1

Size

200 B

Version

2

Bits

0acf8488

Nonce

1,915,155,104

Timestamp

12/16/2015, 5:53:43 PM

Confirmations

5,471,142

Mined by

⛏️ P2SHAbibk41G8eqH2yXAEXprUJTuNR5bNL7ALS

Merkle Root

c2eb79e0f7d83841ff71da098a0a3298210149ab2a089325e2563d25a4e23242
Transactions (1)
Coinbasec2eb79e0f7d838…563d25a4e23242
1 in β†’ 1 out8.5400 XPM110 B
Abibk41G…5bNL7ALS
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.

2.456 Γ— 10⁹³(94-digit number)
24567808226865984055…52173626202988815199
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
2.456 Γ— 10⁹³(94-digit number)
24567808226865984055…52173626202988815199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.456 Γ— 10⁹³(94-digit number)
24567808226865984055…52173626202988815201
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
4.913 Γ— 10⁹³(94-digit number)
49135616453731968110…04347252405977630399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.913 Γ— 10⁹³(94-digit number)
49135616453731968110…04347252405977630401
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
9.827 Γ— 10⁹³(94-digit number)
98271232907463936221…08694504811955260799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.827 Γ— 10⁹³(94-digit number)
98271232907463936221…08694504811955260801
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
1.965 Γ— 10⁹⁴(95-digit number)
19654246581492787244…17389009623910521599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.965 Γ— 10⁹⁴(95-digit number)
19654246581492787244…17389009623910521601
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
3.930 Γ— 10⁹⁴(95-digit number)
39308493162985574488…34778019247821043199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.930 Γ— 10⁹⁴(95-digit number)
39308493162985574488…34778019247821043201
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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