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Block #3,037,472

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2019, 8:56:53 PM Β· Difficulty 11.0074 Β· 3,807,828 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4cf302469b91b098b2cc451d4bfa2912410d17482ae5769d91ae201051a52c1b
View on Chainz β†—

Height

#3,037,472

Difficulty

11.007384

Transactions

1

Size

200 B

Version

2

Bits

0b01e3e9

Nonce

870,927,682

Timestamp

2/3/2019, 8:56:53 PM

Confirmations

3,807,828

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

62cbc25960b55cdea46f97758940f770764b75ebe52cc7900ce7bbea0e6f5e52
Transactions (1)
Coinbase62cbc25960b55c…e7bbea0e6f5e52
1 in β†’ 1 out8.2400 XPM110 B
AbXwmGxD…4XXYP765
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.

5.559 Γ— 10⁹⁴(95-digit number)
55598702173584139964…84316461522660324479
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
5.559 Γ— 10⁹⁴(95-digit number)
55598702173584139964…84316461522660324479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.559 Γ— 10⁹⁴(95-digit number)
55598702173584139964…84316461522660324481
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
1.111 Γ— 10⁹⁡(96-digit number)
11119740434716827992…68632923045320648959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.111 Γ— 10⁹⁡(96-digit number)
11119740434716827992…68632923045320648961
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
2.223 Γ— 10⁹⁡(96-digit number)
22239480869433655985…37265846090641297919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.223 Γ— 10⁹⁡(96-digit number)
22239480869433655985…37265846090641297921
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
4.447 Γ— 10⁹⁡(96-digit number)
44478961738867311971…74531692181282595839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.447 Γ— 10⁹⁡(96-digit number)
44478961738867311971…74531692181282595841
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
8.895 Γ— 10⁹⁡(96-digit number)
88957923477734623943…49063384362565191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.895 Γ— 10⁹⁡(96-digit number)
88957923477734623943…49063384362565191681
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
1.779 Γ— 10⁹⁢(97-digit number)
17791584695546924788…98126768725130383359
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:58,006,839 XPMΒ·at block #6,845,299 Β· updates every 60s
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