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Block #2,113,381

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/12/2017, 11:14:45 PM Β· Difficulty 10.8988 Β· 4,729,450 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6bc6bb34f0025b2d08fc10aac8f3c45c6be4fac742199a9b4ec7bc74f64b3a91
View on Chainz β†—

Height

#2,113,381

Difficulty

10.898758

Transactions

2

Size

866 B

Version

2

Bits

0ae61500

Nonce

275,142,001

Timestamp

5/12/2017, 11:14:45 PM

Confirmations

4,729,450

Mined by

⛏️ P2SHAef8MsrVpkL2WZJwc3bjqsmUsdMq6p5iaw

Merkle Root

0c9f9b71ab4e28b6608327633e0ea60c3c0797ef19501ffa780a97e3efbfd90f
Transactions (2)
Coinbasead1b3ce4678c20…38edf1354146dd
1 in β†’ 1 out8.4200 XPM109 B
Aef8MsrV…Mq6p5iaw
c15aa06e2a8e70…f641843a8d32a0
4 in β†’ 2 out1929.0895 XPM667 B
AUfiNpNR…r4iERJXeAKUCky4F…mkqJ34S6
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.

1.166 Γ— 10⁹⁴(95-digit number)
11664127191237049018…13789393044192018429
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
1.166 Γ— 10⁹⁴(95-digit number)
11664127191237049018…13789393044192018429
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.166 Γ— 10⁹⁴(95-digit number)
11664127191237049018…13789393044192018431
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
2.332 Γ— 10⁹⁴(95-digit number)
23328254382474098036…27578786088384036859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.332 Γ— 10⁹⁴(95-digit number)
23328254382474098036…27578786088384036861
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
4.665 Γ— 10⁹⁴(95-digit number)
46656508764948196072…55157572176768073719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.665 Γ— 10⁹⁴(95-digit number)
46656508764948196072…55157572176768073721
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
9.331 Γ— 10⁹⁴(95-digit number)
93313017529896392144…10315144353536147439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.331 Γ— 10⁹⁴(95-digit number)
93313017529896392144…10315144353536147441
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
1.866 Γ— 10⁹⁡(96-digit number)
18662603505979278428…20630288707072294879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.866 Γ— 10⁹⁡(96-digit number)
18662603505979278428…20630288707072294881
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
3.732 Γ— 10⁹⁡(96-digit number)
37325207011958556857…41260577414144589759
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:57,986,991 XPMΒ·at block #6,842,830 Β· updates every 60s
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