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Block #1,612,234

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 10:28:19 AM Β· Difficulty 10.6027 Β· 5,228,229 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6f07007c7bdb1261449166959736c8e75a9617055c5fd5f72ac8aeeabff14e35
View on Chainz β†—

Height

#1,612,234

Difficulty

10.602685

Transactions

1

Size

199 B

Version

2

Bits

0a9a4995

Nonce

1,207,160,645

Timestamp

6/3/2016, 10:28:19 AM

Confirmations

5,228,229

Mined by

⛏️ P2SHAKWYWX5gC9nCTd4LmRrxxsMwwK18nBz4GD

Merkle Root

32c628494d854b6e2cf6f56838fd74c2a350bf7a3590e27cbc3c10416f495c1e
Transactions (1)
Coinbase32c628494d854b…3c10416f495c1e
1 in β†’ 1 out8.8800 XPM109 B
AKWYWX5g…18nBz4GD
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.

1.055 Γ— 10⁹⁡(96-digit number)
10555653308555394351…75396178527439175679
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
1.055 Γ— 10⁹⁡(96-digit number)
10555653308555394351…75396178527439175679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.055 Γ— 10⁹⁡(96-digit number)
10555653308555394351…75396178527439175681
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
2.111 Γ— 10⁹⁡(96-digit number)
21111306617110788702…50792357054878351359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.111 Γ— 10⁹⁡(96-digit number)
21111306617110788702…50792357054878351361
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
4.222 Γ— 10⁹⁡(96-digit number)
42222613234221577405…01584714109756702719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.222 Γ— 10⁹⁡(96-digit number)
42222613234221577405…01584714109756702721
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
8.444 Γ— 10⁹⁡(96-digit number)
84445226468443154811…03169428219513405439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.444 Γ— 10⁹⁡(96-digit number)
84445226468443154811…03169428219513405441
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
1.688 Γ— 10⁹⁢(97-digit number)
16889045293688630962…06338856439026810879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.688 Γ— 10⁹⁢(97-digit number)
16889045293688630962…06338856439026810881
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:57,968,032 XPMΒ·at block #6,840,462 Β· updates every 60s
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