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Block #3,140,127

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/15/2019, 8:39:14 AM Β· Difficulty 11.3088 Β· 3,703,873 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9899143b4bac8e1b572cdb2f76dc5565002f9833dd6715b7cca9eba18f10c948
View on Chainz β†—

Height

#3,140,127

Difficulty

11.308844

Transactions

1

Size

199 B

Version

2

Bits

0b4f1065

Nonce

624,740,490

Timestamp

4/15/2019, 8:39:14 AM

Confirmations

3,703,873

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

754d44bb91cfb49efc9461268533a829f0b63c9becdabc5fe2f55eb7c8dcb2e0
Transactions (1)
Coinbase754d44bb91cfb4…f55eb7c8dcb2e0
1 in β†’ 1 out7.8100 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.

1.205 Γ— 10⁹²(93-digit number)
12052587834562065448…47820741671805851159
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
1.205 Γ— 10⁹²(93-digit number)
12052587834562065448…47820741671805851159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.205 Γ— 10⁹²(93-digit number)
12052587834562065448…47820741671805851161
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
2.410 Γ— 10⁹²(93-digit number)
24105175669124130896…95641483343611702319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.410 Γ— 10⁹²(93-digit number)
24105175669124130896…95641483343611702321
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
4.821 Γ— 10⁹²(93-digit number)
48210351338248261792…91282966687223404639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.821 Γ— 10⁹²(93-digit number)
48210351338248261792…91282966687223404641
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
9.642 Γ— 10⁹²(93-digit number)
96420702676496523585…82565933374446809279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.642 Γ— 10⁹²(93-digit number)
96420702676496523585…82565933374446809281
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
1.928 Γ— 10⁹³(94-digit number)
19284140535299304717…65131866748893618559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.928 Γ— 10⁹³(94-digit number)
19284140535299304717…65131866748893618561
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
3.856 Γ— 10⁹³(94-digit number)
38568281070598609434…30263733497787237119
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:57,996,382 XPMΒ·at block #6,843,999 Β· updates every 60s
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