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Block #1,924,938

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/5/2017, 11:28:14 AM Β· Difficulty 10.7235 Β· 4,887,754 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f5fc8e5cb073320661e45505c5138a08bc83e8f56df28e4adae4876d5d11f75
View on Chainz β†—

Height

#1,924,938

Difficulty

10.723514

Transactions

2

Size

835 B

Version

2

Bits

0ab93832

Nonce

11,264,029

Timestamp

1/5/2017, 11:28:14 AM

Confirmations

4,887,754

Mined by

⛏️ P2SHAFt8jX1ikWM7RNnkX6SS6VQsJWUbEpSAeP

Merkle Root

094a66fa7f868a1795a56815eeb1e31f21ac569e109a11311994b86f126a3457
Transactions (2)
Coinbasec2f98640d0e60f…59fd4a5f5f256a
1 in β†’ 1 out8.6900 XPM109 B
AFt8jX1i…UbEpSAeP
f3ef69aed9f18f…007ed51f3e0d9a
4 in β†’ 1 out1380.0400 XPM637 B
ALjVzEH6…ZtoUaFFi
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.

2.321 Γ— 10⁹²(93-digit number)
23210159162667218851…77521559935654067199
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
2.321 Γ— 10⁹²(93-digit number)
23210159162667218851…77521559935654067199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.321 Γ— 10⁹²(93-digit number)
23210159162667218851…77521559935654067201
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
4.642 Γ— 10⁹²(93-digit number)
46420318325334437703…55043119871308134399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.642 Γ— 10⁹²(93-digit number)
46420318325334437703…55043119871308134401
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
9.284 Γ— 10⁹²(93-digit number)
92840636650668875407…10086239742616268799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.284 Γ— 10⁹²(93-digit number)
92840636650668875407…10086239742616268801
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
1.856 Γ— 10⁹³(94-digit number)
18568127330133775081…20172479485232537599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.856 Γ— 10⁹³(94-digit number)
18568127330133775081…20172479485232537601
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
3.713 Γ— 10⁹³(94-digit number)
37136254660267550163…40344958970465075199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.713 Γ— 10⁹³(94-digit number)
37136254660267550163…40344958970465075201
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:57,745,571 XPMΒ·at block #6,812,691 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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