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Block #2,094,188

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2017, 10:55:24 AM Β· Difficulty 10.8715 Β· 4,732,370 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
79005a0bbf8a9cb6ab9b8b44422d7267d1c2e154e9f3fa5192c833598afe5404
View on Chainz β†—

Height

#2,094,188

Difficulty

10.871528

Transactions

2

Size

426 B

Version

2

Bits

0adf1c78

Nonce

490,254,234

Timestamp

4/30/2017, 10:55:24 AM

Confirmations

4,732,370

Mined by

⛏️ P2SHAHMwwH5QsbaKNfYGvGzJFqu41oS7vR2WBV

Merkle Root

55e6a2bcb1e757a91c79ee74c7b38e81a551494331f8241556fab3c13e42fe2f
Transactions (2)
Coinbase5d30476a09920d…4fc150aaced7a2
1 in β†’ 1 out8.4600 XPM109 B
AHMwwH5Q…S7vR2WBV
bb21ed5b4fd369…54ac8637bf0fbe
1 in β†’ 2 out225001.0900 XPM226 B
AZDAsw8P…hW3PZZstAGb1CEWm…s2S7Hx1M
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.

8.604 Γ— 10⁹⁢(97-digit number)
86046760255727297709…02995565007625256959
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
8.604 Γ— 10⁹⁢(97-digit number)
86046760255727297709…02995565007625256959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.604 Γ— 10⁹⁢(97-digit number)
86046760255727297709…02995565007625256961
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
1.720 Γ— 10⁹⁷(98-digit number)
17209352051145459541…05991130015250513919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.720 Γ— 10⁹⁷(98-digit number)
17209352051145459541…05991130015250513921
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
3.441 Γ— 10⁹⁷(98-digit number)
34418704102290919083…11982260030501027839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.441 Γ— 10⁹⁷(98-digit number)
34418704102290919083…11982260030501027841
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
6.883 Γ— 10⁹⁷(98-digit number)
68837408204581838167…23964520061002055679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.883 Γ— 10⁹⁷(98-digit number)
68837408204581838167…23964520061002055681
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
1.376 Γ— 10⁹⁸(99-digit number)
13767481640916367633…47929040122004111359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.376 Γ— 10⁹⁸(99-digit number)
13767481640916367633…47929040122004111361
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:57,856,615 XPMΒ·at block #6,826,557 Β· updates every 60s
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