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Block #2,102,988

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2017, 1:19:33 PM Β· Difficulty 10.8722 Β· 4,739,369 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8b50fa8a47bb94d26521a28b5d31cd48d66bb93f290c47eaa56b90386af10e4
View on Chainz β†—

Height

#2,102,988

Difficulty

10.872216

Transactions

1

Size

200 B

Version

2

Bits

0adf4992

Nonce

718,824,818

Timestamp

5/6/2017, 1:19:33 PM

Confirmations

4,739,369

Mined by

⛏️ P2SHALbAjpCq9oznVWv1DK7SuhJmroNHm3Bq1T

Merkle Root

efb2c93eb633819b4e733f06cbffe5c8eca93ece42bbc9cf5fc9fe9e0103ddbf
Transactions (1)
Coinbaseefb2c93eb63381…c9fe9e0103ddbf
1 in β†’ 1 out8.4500 XPM109 B
ALbAjpCq…NHm3Bq1T
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.

3.525 Γ— 10⁹⁷(98-digit number)
35257509959563469561…20268304964052602879
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
3.525 Γ— 10⁹⁷(98-digit number)
35257509959563469561…20268304964052602879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.525 Γ— 10⁹⁷(98-digit number)
35257509959563469561…20268304964052602881
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
7.051 Γ— 10⁹⁷(98-digit number)
70515019919126939122…40536609928105205759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.051 Γ— 10⁹⁷(98-digit number)
70515019919126939122…40536609928105205761
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
1.410 Γ— 10⁹⁸(99-digit number)
14103003983825387824…81073219856210411519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.410 Γ— 10⁹⁸(99-digit number)
14103003983825387824…81073219856210411521
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
2.820 Γ— 10⁹⁸(99-digit number)
28206007967650775649…62146439712420823039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.820 Γ— 10⁹⁸(99-digit number)
28206007967650775649…62146439712420823041
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
5.641 Γ— 10⁹⁸(99-digit number)
56412015935301551298…24292879424841646079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.641 Γ— 10⁹⁸(99-digit number)
56412015935301551298…24292879424841646081
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:57,983,263 XPMΒ·at block #6,842,356 Β· updates every 60s
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