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Block #2,127,670

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/22/2017, 4:11:48 AM Β· Difficulty 10.9179 Β· 4,703,731 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d73c9e102ab93cc81ab66857265bc290b8331f330f04af5d9d7b3fa868b9fced
View on Chainz β†—

Height

#2,127,670

Difficulty

10.917901

Transactions

3

Size

1.24 KB

Version

2

Bits

0aeafb91

Nonce

498,415,163

Timestamp

5/22/2017, 4:11:48 AM

Confirmations

4,703,731

Mined by

⛏️ P2SHAKBZny54hAZgnFqMcrjyRpkxt8CYN6pNW8

Merkle Root

421d069e3abde5f0be01f187956489aa2e54d13707aec6f3d82a7698b9ef5744
Transactions (3)
Coinbasec3f585c8c7d626…68f49b5cddeb63
1 in β†’ 1 out8.4000 XPM109 B
AKBZny54…CYN6pNW8
7a953e20f5d20d…81b4eb668c04e7
7 in β†’ 2 out58.6800 XPM876 B
ARvBNTcz…td1iNyXNAdQVyW6h…woPp73cj
e5c83d9f1407e3…a53124c3ddea2e
1 in β†’ 1 out0.5380 XPM191 B
AdTRX9fd…4mbpZ6FA
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.

4.850 Γ— 10⁹⁴(95-digit number)
48501051205728489455…65773468286253847999
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
4.850 Γ— 10⁹⁴(95-digit number)
48501051205728489455…65773468286253847999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.850 Γ— 10⁹⁴(95-digit number)
48501051205728489455…65773468286253848001
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
9.700 Γ— 10⁹⁴(95-digit number)
97002102411456978911…31546936572507695999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.700 Γ— 10⁹⁴(95-digit number)
97002102411456978911…31546936572507696001
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
1.940 Γ— 10⁹⁡(96-digit number)
19400420482291395782…63093873145015391999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.940 Γ— 10⁹⁡(96-digit number)
19400420482291395782…63093873145015392001
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
3.880 Γ— 10⁹⁡(96-digit number)
38800840964582791564…26187746290030783999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.880 Γ— 10⁹⁡(96-digit number)
38800840964582791564…26187746290030784001
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
7.760 Γ— 10⁹⁡(96-digit number)
77601681929165583129…52375492580061567999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.760 Γ— 10⁹⁡(96-digit number)
77601681929165583129…52375492580061568001
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:57,895,365 XPMΒ·at block #6,831,400 Β· updates every 60s
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