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Block #2,118,826

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2017, 8:52:04 AM Β· Difficulty 10.9093 Β· 4,723,391 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c17b18759dccd50006a199214078b2e1fbf47ede2a5dceb5b0247f9007398052
View on Chainz β†—

Height

#2,118,826

Difficulty

10.909315

Transactions

1

Size

242 B

Version

2

Bits

0ae8c8e6

Nonce

464,183,991

Timestamp

5/16/2017, 8:52:04 AM

Confirmations

4,723,391

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

d2f1cd68ba39d5162bad9aac70844ddde7a348f113f20b544718ffec26cacf5b
Transactions (1)
Coinbased2f1cd68ba39d5…18ffec26cacf5b
1 in β†’ 2 out8.3900 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

6.080 Γ— 10⁹⁴(95-digit number)
60800127455753422633…44704662193283496759
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
6.080 Γ— 10⁹⁴(95-digit number)
60800127455753422633…44704662193283496759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.080 Γ— 10⁹⁴(95-digit number)
60800127455753422633…44704662193283496761
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
1.216 Γ— 10⁹⁡(96-digit number)
12160025491150684526…89409324386566993519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.216 Γ— 10⁹⁡(96-digit number)
12160025491150684526…89409324386566993521
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
2.432 Γ— 10⁹⁡(96-digit number)
24320050982301369053…78818648773133987039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.432 Γ— 10⁹⁡(96-digit number)
24320050982301369053…78818648773133987041
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
4.864 Γ— 10⁹⁡(96-digit number)
48640101964602738106…57637297546267974079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.864 Γ— 10⁹⁡(96-digit number)
48640101964602738106…57637297546267974081
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
9.728 Γ— 10⁹⁡(96-digit number)
97280203929205476213…15274595092535948159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.728 Γ— 10⁹⁡(96-digit number)
97280203929205476213…15274595092535948161
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:57,982,134 XPMΒ·at block #6,842,216 Β· updates every 60s
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