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Block #210,962

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 10/15/2013, 11:24:02 AM Ā· Difficulty 9.9140 Ā· 6,587,970 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c3ac867192321e3630e7968c08ad286916c59b08f10af614e5fdab7b898d2057
View on Chainz ā†—

Height

#210,962

Difficulty

9.914002

Transactions

1

Size

4.10 KB

Version

2

Bits

09e9fc0f

Nonce

1,164,772,883

Timestamp

10/15/2013, 11:24:02 AM

Confirmations

6,587,970

Mined by

ā›ļø 8RAVfaPNpg5592Nx85hNx25cxAKgtW74zY1Y

Merkle Root

d8e81b315c46bdabadeca544689d9fe87e93eb32c4b2f87e7fcd5e4c79cc778f
Transactions (1)
Coinbased8e81b315c46bdā€¦cd5e4c79cc778f
1 in ā†’ 119 out10.1100 XPM4.01 KB
AVfaPNpgā€¦tW74zY1YAGB4r7xvā€¦BBsSHL1wAHqZtsfnā€¦WrCGjM3JAdjTC88Eā€¦1j5RajcsAb7ULbjQā€¦fuVABZZs
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.669 Ɨ 10ā¹āµ(96-digit number)
16698883135235582452ā€¦82922957360021980799
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
1.669 Ɨ 10ā¹āµ(96-digit number)
16698883135235582452ā€¦82922957360021980799
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.669 Ɨ 10ā¹āµ(96-digit number)
16698883135235582452ā€¦82922957360021980801
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
3.339 Ɨ 10ā¹āµ(96-digit number)
33397766270471164905ā€¦65845914720043961599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
3.339 Ɨ 10ā¹āµ(96-digit number)
33397766270471164905ā€¦65845914720043961601
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
6.679 Ɨ 10ā¹āµ(96-digit number)
66795532540942329811ā€¦31691829440087923199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
6.679 Ɨ 10ā¹āµ(96-digit number)
66795532540942329811ā€¦31691829440087923201
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
1.335 Ɨ 10ā¹ā¶(97-digit number)
13359106508188465962ā€¦63383658880175846399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.335 Ɨ 10ā¹ā¶(97-digit number)
13359106508188465962ā€¦63383658880175846401
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
2.671 Ɨ 10ā¹ā¶(97-digit number)
26718213016376931924ā€¦26767317760351692799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
2.671 Ɨ 10ā¹ā¶(97-digit number)
26718213016376931924ā€¦26767317760351692801
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,635,491 XPMĀ·at block #6,798,931 Ā· updates every 60s
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