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Block #2,051,362

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2017, 12:07:48 PM Β· Difficulty 10.7117 Β· 4,791,874 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c53641d08e52ae7250a83da70b1f3691029f2d937a19680d2cf837aff06c8760
View on Chainz β†—

Height

#2,051,362

Difficulty

10.711724

Transactions

1

Size

200 B

Version

2

Bits

0ab6338b

Nonce

14,173,553

Timestamp

4/3/2017, 12:07:48 PM

Confirmations

4,791,874

Mined by

⛏️ P2SHARvuvx7GGoRHBCqCwr4PjF8ZhEqZ2U1ydb

Merkle Root

2d79ae548eacf6213bb4cb83907a152c839a15d4dfd8f9226f43d4fc83957620
Transactions (1)
Coinbase2d79ae548eacf6…43d4fc83957620
1 in β†’ 1 out8.7000 XPM109 B
ARvuvx7G…qZ2U1ydb
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.

9.555 Γ— 10⁹⁡(96-digit number)
95557202776233675788…63182111054108004479
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
9.555 Γ— 10⁹⁡(96-digit number)
95557202776233675788…63182111054108004479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.555 Γ— 10⁹⁡(96-digit number)
95557202776233675788…63182111054108004481
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
1.911 Γ— 10⁹⁢(97-digit number)
19111440555246735157…26364222108216008959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.911 Γ— 10⁹⁢(97-digit number)
19111440555246735157…26364222108216008961
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
3.822 Γ— 10⁹⁢(97-digit number)
38222881110493470315…52728444216432017919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.822 Γ— 10⁹⁢(97-digit number)
38222881110493470315…52728444216432017921
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
7.644 Γ— 10⁹⁢(97-digit number)
76445762220986940631…05456888432864035839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.644 Γ— 10⁹⁢(97-digit number)
76445762220986940631…05456888432864035841
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
1.528 Γ— 10⁹⁷(98-digit number)
15289152444197388126…10913776865728071679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.528 Γ— 10⁹⁷(98-digit number)
15289152444197388126…10913776865728071681
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:57,990,262 XPMΒ·at block #6,843,235 Β· updates every 60s
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