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Block #2,642,642

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 7:34:18 PM Β· Difficulty 11.6595 Β· 4,196,529 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f09e3711a922b7f50123df61b7c53974b51890c1dc5aca7c93f82a9427024af
View on Chainz β†—

Height

#2,642,642

Difficulty

11.659522

Transactions

2

Size

426 B

Version

2

Bits

0ba8d669

Nonce

130,731,508

Timestamp

5/1/2018, 7:34:18 PM

Confirmations

4,196,529

Mined by

⛏️ P2SHAPDbUFk6TLUwoYAvBfXbdGCT1WQQB1W314

Merkle Root

121699377eac4a8dc47da8cb348ecbd508b2a133613a1ba5f4f10747e0989274
Transactions (2)
Coinbase322d3f018b52f7…30b57a454f8b74
1 in β†’ 1 out7.3500 XPM110 B
APDbUFk6…QQB1W314
1df0f03d39ad2e…cad26b03305f69
1 in β†’ 2 out4086.5303 XPM226 B
AVKzWN33…SKmsogJ6AYknzj4R…hV6RW4vA
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.

4.222 Γ— 10⁹⁴(95-digit number)
42227204966671853742…63113417956467843399
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
4.222 Γ— 10⁹⁴(95-digit number)
42227204966671853742…63113417956467843399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.222 Γ— 10⁹⁴(95-digit number)
42227204966671853742…63113417956467843401
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
8.445 Γ— 10⁹⁴(95-digit number)
84454409933343707485…26226835912935686799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.445 Γ— 10⁹⁴(95-digit number)
84454409933343707485…26226835912935686801
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
1.689 Γ— 10⁹⁡(96-digit number)
16890881986668741497…52453671825871373599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.689 Γ— 10⁹⁡(96-digit number)
16890881986668741497…52453671825871373601
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
3.378 Γ— 10⁹⁡(96-digit number)
33781763973337482994…04907343651742747199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.378 Γ— 10⁹⁡(96-digit number)
33781763973337482994…04907343651742747201
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
6.756 Γ— 10⁹⁡(96-digit number)
67563527946674965988…09814687303485494399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.756 Γ— 10⁹⁡(96-digit number)
67563527946674965988…09814687303485494401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁢(97-digit number)
13512705589334993197…19629374606970988799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,957,649 XPMΒ·at block #6,839,170 Β· updates every 60s
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