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Block #2,107,044

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2017, 6:32:05 PM Β· Difficulty 10.8924 Β· 4,736,601 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6cdfd44076f439ab26e89933d8cce1fe48ffe7d099419bc7afd84f4481c740e8
View on Chainz β†—

Height

#2,107,044

Difficulty

10.892432

Transactions

2

Size

424 B

Version

2

Bits

0ae4766a

Nonce

923,607,649

Timestamp

5/8/2017, 6:32:05 PM

Confirmations

4,736,601

Mined by

⛏️ P2SHAYykTfebCFUpxp4ikVvKnnA7gw2zoLyjFJ

Merkle Root

47d051bcc78af46abf258db0c20421719e8161e57805fd3671d61037cfa2190f
Transactions (2)
Coinbase15c823d7bb45f1…a484c826f3a4ba
1 in β†’ 1 out8.4300 XPM109 B
AYykTfeb…2zoLyjFJ
0726dc5a6be1f9…48c370f981b61e
1 in β†’ 2 out38446.8655 XPM225 B
AYpvkhsq…Z2JBoHjYAMp95CH9…npLmKdKa
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.

9.468 Γ— 10⁹⁴(95-digit number)
94684432022811662626…60034042518599677919
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
9.468 Γ— 10⁹⁴(95-digit number)
94684432022811662626…60034042518599677919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.468 Γ— 10⁹⁴(95-digit number)
94684432022811662626…60034042518599677921
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
1.893 Γ— 10⁹⁡(96-digit number)
18936886404562332525…20068085037199355839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.893 Γ— 10⁹⁡(96-digit number)
18936886404562332525…20068085037199355841
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
3.787 Γ— 10⁹⁡(96-digit number)
37873772809124665050…40136170074398711679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.787 Γ— 10⁹⁡(96-digit number)
37873772809124665050…40136170074398711681
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
7.574 Γ— 10⁹⁡(96-digit number)
75747545618249330101…80272340148797423359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.574 Γ— 10⁹⁡(96-digit number)
75747545618249330101…80272340148797423361
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
1.514 Γ— 10⁹⁢(97-digit number)
15149509123649866020…60544680297594846719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.514 Γ— 10⁹⁢(97-digit number)
15149509123649866020…60544680297594846721
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:57,993,530 XPMΒ·at block #6,843,644 Β· updates every 60s
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