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Block #2,501,127

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/1/2018, 6:07:35 PM Β· Difficulty 10.9767 Β· 4,313,772 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d86d3ee5706eb5faf00bf435a3ca3a5a67d21c7ee410da98bdfb028bd2b997b
View on Chainz β†—

Height

#2,501,127

Difficulty

10.976715

Transactions

1

Size

201 B

Version

2

Bits

0afa09f8

Nonce

2,101,575,314

Timestamp

2/1/2018, 6:07:35 PM

Confirmations

4,313,772

Mined by

⛏️ P2SHAR5UkWTVYEkKUFJvGHj1RZDyEDSiPT3jsn

Merkle Root

9fda7ce95fe5b2dbcb8b542c850d0179e9e642db31100d4e2a895f33e480b119
Transactions (1)
Coinbase9fda7ce95fe5b2…895f33e480b119
1 in β†’ 1 out8.2900 XPM110 B
AR5UkWTV…SiPT3jsn
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.

9.249 Γ— 10⁹⁷(98-digit number)
92491059253469353697…49709592869541642239
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
9.249 Γ— 10⁹⁷(98-digit number)
92491059253469353697…49709592869541642239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.249 Γ— 10⁹⁷(98-digit number)
92491059253469353697…49709592869541642241
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
1.849 Γ— 10⁹⁸(99-digit number)
18498211850693870739…99419185739083284479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.849 Γ— 10⁹⁸(99-digit number)
18498211850693870739…99419185739083284481
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
3.699 Γ— 10⁹⁸(99-digit number)
36996423701387741478…98838371478166568959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.699 Γ— 10⁹⁸(99-digit number)
36996423701387741478…98838371478166568961
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
7.399 Γ— 10⁹⁸(99-digit number)
73992847402775482957…97676742956333137919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.399 Γ— 10⁹⁸(99-digit number)
73992847402775482957…97676742956333137921
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
1.479 Γ— 10⁹⁹(100-digit number)
14798569480555096591…95353485912666275839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.479 Γ— 10⁹⁹(100-digit number)
14798569480555096591…95353485912666275841
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:57,763,281 XPMΒ·at block #6,814,898 Β· updates every 60s
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