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Block #1,732,920

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2016, 1:26:57 AM Β· Difficulty 10.7211 Β· 5,078,029 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c10f9e4d9c392410c6f8e960f35da0f2f9874840be6faffb7a5cb30085df998b
View on Chainz β†—

Height

#1,732,920

Difficulty

10.721109

Transactions

1

Size

242 B

Version

2

Bits

0ab89aa0

Nonce

730,780,710

Timestamp

8/25/2016, 1:26:57 AM

Confirmations

5,078,029

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

b105b06635feaf8f2dde7a4c3046d6004d94b383cdc29212a15bdaecf7864253
Transactions (1)
Coinbaseb105b06635feaf…5bdaecf7864253
1 in β†’ 2 out8.6900 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

1.178 Γ— 10⁹⁡(96-digit number)
11781297681865348911…35566431696639867799
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
1.178 Γ— 10⁹⁡(96-digit number)
11781297681865348911…35566431696639867799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.178 Γ— 10⁹⁡(96-digit number)
11781297681865348911…35566431696639867801
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
2.356 Γ— 10⁹⁡(96-digit number)
23562595363730697823…71132863393279735599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.356 Γ— 10⁹⁡(96-digit number)
23562595363730697823…71132863393279735601
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
4.712 Γ— 10⁹⁡(96-digit number)
47125190727461395647…42265726786559471199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.712 Γ— 10⁹⁡(96-digit number)
47125190727461395647…42265726786559471201
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
9.425 Γ— 10⁹⁡(96-digit number)
94250381454922791294…84531453573118942399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.425 Γ— 10⁹⁡(96-digit number)
94250381454922791294…84531453573118942401
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
1.885 Γ— 10⁹⁢(97-digit number)
18850076290984558258…69062907146237884799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.885 Γ— 10⁹⁢(97-digit number)
18850076290984558258…69062907146237884801
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:57,731,690 XPMΒ·at block #6,810,948 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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