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Block #2,207,421

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2017, 5:52:11 AM Β· Difficulty 10.9454 Β· 4,637,668 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c70711269d5103336c31a3cc04fb0435b484911258bcbcb90ff6e9572cc79092
View on Chainz β†—

Height

#2,207,421

Difficulty

10.945408

Transactions

1

Size

200 B

Version

2

Bits

0af2063c

Nonce

356,916,187

Timestamp

7/15/2017, 5:52:11 AM

Confirmations

4,637,668

Mined by

⛏️ P2SHANG4Yk9oEzyTvUPRsKZMoRXgWCs6t86s3M

Merkle Root

b9ee296d597fabea92759de63098d9ca32e843cb530a0928e8d9d9342dab122b
Transactions (1)
Coinbaseb9ee296d597fab…d9d9342dab122b
1 in β†’ 1 out8.3300 XPM109 B
ANG4Yk9o…s6t86s3M
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.

5.440 Γ— 10⁹⁷(98-digit number)
54403482203137782065…23233129189789409279
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
5.440 Γ— 10⁹⁷(98-digit number)
54403482203137782065…23233129189789409279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.440 Γ— 10⁹⁷(98-digit number)
54403482203137782065…23233129189789409281
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
1.088 Γ— 10⁹⁸(99-digit number)
10880696440627556413…46466258379578818559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.088 Γ— 10⁹⁸(99-digit number)
10880696440627556413…46466258379578818561
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
2.176 Γ— 10⁹⁸(99-digit number)
21761392881255112826…92932516759157637119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.176 Γ— 10⁹⁸(99-digit number)
21761392881255112826…92932516759157637121
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
4.352 Γ— 10⁹⁸(99-digit number)
43522785762510225652…85865033518315274239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.352 Γ— 10⁹⁸(99-digit number)
43522785762510225652…85865033518315274241
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
8.704 Γ— 10⁹⁸(99-digit number)
87045571525020451304…71730067036630548479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.704 Γ— 10⁹⁸(99-digit number)
87045571525020451304…71730067036630548481
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
1.740 Γ— 10⁹⁹(100-digit number)
17409114305004090260…43460134073261096959
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:58,005,140 XPMΒ·at block #6,845,088 Β· updates every 60s
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